Crouch, who launched the review that concluded that FOBT stakes should be slashed from £100 to £2, quit after the chancellor revealed in this week’s budget that the change would not take effect until October next year. The Conservative MP had lobbied hard for the cut to be implemented as soon as possible, in April 2019.

The comment is thought to be a reference to lobbying efforts by MPs with ties to the betting industry to postpone the cut in stakes.

“From the time of the announcement to reduce stakes and its implementation, £1.6bn will be lost on these machines, a significant amount of which will be in our most deprived areas, including my own constituency,” Crouch wrote. “In addition, two people will tragically take their lives every day due to gambling-related problems and for that reason as much as any other I believe this delay is unjustifiable.”

She added that “ministers must adhere to collective responsibility and cannot disagree with policy, let alone when it’s policy made against your wishes relating to your own portfolio”.

In her response, Theresa May contradicted Crouch, saying there had been “no delay”. She wrote that the government had “listened to those who wanted it to come into effect earlier than April 2020 and have agreed that changes should be in place within the year – by October 2019”.

Crouch is understood to have clashed with Jeremy Wright, the minister for the department for digital, culture, media and sport (DCMS), over the delay, with the sports minister insisting that April 2019 was a red line for her.

Prior to this week’s announcement, she had repeatedly said on the record that the step would be put before MPs before next week’s parliamentary recess and introduced by next April. That raised the possibility the minister had either been cut out of the decision or overruled on it.

Tracey Crouch (@tracey_crouch)

It is with great sadness I have resigned from one of the best jobs in Government. Thank you so much for all the very kind messages of support I have received throughout the day. Politicians come and go but principles stay with us forever. pic.twitter.com/rD8bEbCQcK

The six-month postponement, which will allow bookmakers to collect an extra £900m from the machines, has also sparked outcry among campaigners and MPs.

Wright defended the delay in parliament on Thursday in the face of fierce criticism from both sides of the house, including from the former Tory leader, Iain Duncan Smith. Duncan Smith later invited the chief secretary to the Treasury, Liz Truss, to consider bringing forward the cut in the House of Commons on Thursday evening, amid speculation that Crouch’s threat to resign had forced the government into a U-turn.

Truss said: “I don’t believe it’s an issue for the finance bill, but I’m happy to discuss with my honourable friend about what more we can do.”

Crouch is now likely to add her name to a planned amendment to the finance bill, the act that implements the budget. Duncan Smith and Labour MP Carolyn Harris are expected to lay the amendment, which is believed to have the support of about 35 Tory rebels, leaving the government facing the prospect of a bruising defeat.

The archbishop of Canterbury praised her stance over FOBTs on Thursday night. Justin Welby tweeted that Crouch was “principled and courageous … May God bless her commitment to doing right”. People close to Crouch said her resolve had been hardened by meetings with the parents of children who took their own lives after becoming addicting to gambling through FOBTs.

In a letter to Philip Hammond, some of the parents who Crouch met told the chancellor he would be “morally bankrupt” if he allowed bookies to maintain FOBTs at £100 a spin until October.

The Gambling With Lives group told Hammond that “FOBTs were an instrumental factor in our children’s deaths”. “Every month the reduced stake implementation is delayed sees tens of thousands more young people becoming addicted, and dozens of gambling-related suicides.

“The chancellor would be morally bankrupt should he continue to side with the bookmakers and allow them to profit at the expense of young people’s lives. How many more lives need to be lost before the government finally acts and implements the reduced FOBT stake?”

Labour’s deputy leader and shadow DCMS minister Tom Watson said: “Tracey Crouch has taken a courageous and principled decision to resign from the government over Jeremy Wright’s decision to delay cutting the maximum stake on FOBTs.

“She poured her heart and soul into a significant review of these destructive machines, faced down a systematic lobbying attempt by the gambling industry, and took the right decision for those suffering from problem gambling, their families and communities.

“The new secretary of state has threatened all of this good work. He has prioritised corporate interests over victims, profits over public health and greed over good. He should be thoroughly ashamed.”

Speaking in the House of Commons earlier, Wright said the stake cut had not been delayed but had in fact been brought forward from an earlier planned date of April 2020. He said the gambling industry needed time to prepare for the economic impact of the changes.

FOBTs are worth about £1.8bn a year to bookmakers, who have warned of shop closures and thousands of a job losses as a result of stakes being cut to £2.

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The Treasury also expects to lose £1.15bn in taxes over five years due to the decision and has said it will pay for this by increasing the tax on online gambling from 15% to 21%, raising £1.225bn over the same period.

Wright said the delay was not just about giving bookmakers time to absorb the impact of FOBT curbs, but also to allow online operators to prepare for their increased tax burden.

A spokesperson for charity Christian Action Research and Education (Care) said: “This all looks like there has been a dodgy backroom deal done with the bookies at the expense of communities and problem gamblers that will lose out with this delay. The idea that bookies need more time to prepare is simply absurd when weighed up against the profits that they will bank because of this delay.”